Recent technological advances in representation of processes in numerical climate models have led to skillful predictions, which can consequently increase the confidence of hydrological predictions and usability of hydroclimatic services. Given that many water‐related stakeholders are affected by seasonal hydrological variations, there is a need to manage such variations to their advantage through better understanding of the drivers that influence hydrological predictability. Here we analyze the seasonal forecasts of streamflow volumes across about 35,400 basins in Europe, which lie along a strong gradient in terms of climatology, scale, and hydrological regime. We then link the seasonal volumetric errors to various physiographic‐hydroclimatic descriptors and meteorological biases in order to identify the key drivers controlling predictability. Streamflow volumes over Europe are well predicted, yet with some geographic and seasonal variability; however, the predictability deteriorates with increasing lead time particularly in the winter months. Nevertheless, we show that the forecast quality is well correlated to a set of descriptors, which vary depending on the initialization month. The forecast quality of seasonal streamflow volumes is strongly dependent on the basin's hydrological regime, with limited predictability in relatively flashy basins. On the contrary, snow and/or baseflow dominated regions with long recessions show high streamflow predictability. Finally, climatology and precipitation forecast biases are also related to streamflow predictability, highlighting the importance of developing robust bias adjustment methods. Overall, this investigation shows that the seasonal streamflow predictability can be clustered, and hence regionalized, based on a priori knowledge of local hydroclimatic conditions.